Question: Simplify. Rewrite the expression in the form $a^n$. $a^0\cdot a^6=$
$\begin{aligned} a^0\cdot a^6&=a^{0+6} \\\\ &=a^{6} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} a^0\cdot a^6&=\underbrace{1}_{a^0}\cdot\underbrace{a\cdot a\cdot a\cdot a\cdot a\cdot a}_\text{6 times} \\\\\\ &=\underbrace{a\cdot a\cdot a\cdot a\cdot a\cdot a}_\text{6 times} \\\\ &=a^{6} \end{aligned}$ In conclusion, $a^0\cdot a^6=a^{6}$.